Question

A Broadway musical was attended by a total of 2,838 people, including men, women, and children. The number of women who attended the event was 5 more than 3 times the number of children, while the number of men was 3 less than 4 times the number of women. Write an equation to model this situation. Then, use the equation to find the number of men, women, and children who attended the musical

Answer 1

Let x represents the number of children in the Broadway musical,

Since, The number of women who attended the event was 5 more than 3 times the number of children,

⇒ The number of women = 3x + 5

Also, the number of men was 3 less than 4 times the number of women,

⇒ The number of men = 4(3x+5)-3 = 12x + 20 - 3 = 12x + 17

Thus, the total number of persons = x + 3x + 5 + 12x + 17 = 16x + 22

According to the question,

16x + 22 = 2838

Which is the required equation,

Subtract 22 on both sides,

16x = 2816 ⇒ x = 176

Hence, the total number of children = 176

The number of women = 3 × 176 + 5 = 533

And, the number of men = 12 × 176 + 17 = 2129